Why not extend the question a bit? Given p, q and b, how many digits of base b will be required in the repeat? The answer could be an infinite number.
On Wed, Jul 23, 2014 at 5:15 AM, Raul Miller <[email protected]> wrote: > OK, rereading the original post, I guess I should assume that we are not > only interested in the decimal case. > > That said, I'm not certain that it makes sense to assume that the least > common denominator has been factored out of p and q, either. > > -- > Raul > On Jul 23, 2014 1:28 AM, "greg heil" <[email protected]> wrote: > > > Raul > > > > >Well the way i read Dans query only q and b are important... so if > > bq=:([:q:])-.([:q:[) > > then a null result would be finite, eg > > 3 bq 3 > > 10 bq 3 > > 3 > > > > greg > > ~krsnadas.org > > > > -- > > > > from: Raul Miller <[email protected]> > > reply-to: [email protected] > > to: Chat forum <[email protected]> > > date: 22 July 2014 20:42 > > subject: Re: [Jchat] Repeating decimals > > > > That's an interesting point. > > > > >Nevertheless, given the subject line of this thread, I think that maybe > > the base has already been determined. > > > > Thanks, > > > > -- > > Raul > > > > -- > > > > from: greg heil <[email protected]> > > to: Chat forum <[email protected]> > > date: 22 July 2014 19:42 > > subject: Re: [Jchat] Repeating decimals > > > > >What ever formula would also depend on b ... eg the division of 1 by 3 > > has a finite representation in base 3 of 0.1. (although its > representation > > in base 10 is infinite) > > > > greg > > ~krsnadas.org > > > > -- > > > > from: Raul Miller <[email protected]> > > to: Chat forum <[email protected]> > > date: 22 July 2014 10:18 > > subject: Re: [Jchat] Repeating decimals > > > > $p(2 5-.~[:q:]%+.)q > > 0 > > > > >Assuming p and q are rank 0, of course. (And this is a reasonable > > assumption, since the problem statement suggests no use for dimensions). > > > > Thanks, > > > > -- > > Raul > > > > -- > > > > from: Dan Bron <[email protected]> > > to: [email protected] > > date: 22 July 2014 08:25 > > subject: [Jchat] Repeating decimals > > > > >Given 3 positive integers p,q and b, where p and q represent the > > numerator and denominator of a rational number (respectively), and b a > > numerical base (or radix), how can we know if p%q has a finite (or not) > > representation in b? > > > > >In other words, if p%q can be represented by a finite > > (non-infinitely-repeating) decimal in base b, then what do we know about > > the relationship of p to q or p%q to b ? > > > > >You may allow p to take on the value 0 if needed for generality, but q > is > > strictly > 0 (obviously) and b is strictly > 1 (probably?). > > > > -Dan > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
